For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 60 professional actors, it was found that 36 were extroverts. (a)  Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.) (b)  Find a 95% confidence interval for p. (Round your answers to two decimal places.) lower limit          upper limit          Give a brief interpretation of the meaning of the confidence interval you have found. We are 5% confident that the true proportion of actors who are extroverts falls above this interval. We are 95% confident that the true proportion of actors who are extroverts falls within this interval.  We are 95% confident that the true proportion of actors who are extroverts falls outside this interval. We are 5% confident that the true proportion of actors who are extroverts falls within this interval. (c)  Do you think the conditions n·p > 5 and n·q > 5 are satisfied in this problem? Explain why this would be an important consideration. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomia

If we find a 95% confidence interval using a sample, then we can say... 95% of individuals will fall on that interval there is a 5% chance the population proportion is NOT on the interval. 95% of our samples will fall on that interval. No answer text provided.

A College Alcohol Study interviewed an SRS of 1000 college students about their drinking habits. Suppose that half of all college students "drink to get drunk" at least once in a while. That is sample proportion, p-hat 0.5. %3D 9. Estimate a 95% confidence interval for the actual percentage among all students. Round the number to nearest hundredth. O47% to 53% O 50% to 55% 43% to 52% O 44% to 56%

You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 378 randomly selected caterpillars observed, 45 lived to become butterflies. Round answers to 4 decimal places where possible. a.  With 90% confidence the proportion of all caterpillars that lived to become a butterfly is between      and   . b.  If many groups of 378 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About         percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and           about  percent will not contain the true population proportion.